How can you change the rotation of a mirror modifier?
This is not a direct solution to your problem (that really sounds like an "Apply rotation" problem), but it is a work-around that might allow you to achieve what you want.


Remove the Mirror modifier and instead add an Array modifier.
Add an Empty at the location of the original object.
Set the Empty as Object Offset in the Array modifier.
Rotate the Empty until you get a desired rotation.